Temperature-induced polymorphism in methyl stearate

Article abstract of DOI:10.1039/c8ce01055b

The crystallisation of methyl stearate under a range of crystallisation conditions has been studied and three new polymorphs have been identified and structurally characterised. Form III (monoclinic, space group Cc, Z = 8) was obtained at room temperature by slow evaporation of a saturated solution in CS₂. Form IV (monoclinic, space group C2/c, Z = 4) was obtained by slow cooling of the melt. Both structures were characterised by single crystal X-ray diffraction. Form V (monoclinic, space group Cc, Z = 4) was obtained from the melt by rapid cooling. X-ray and neutron powder diffraction methods were employed in the determination of this structure. Form V shows highly anisotropic thermal expansion, with expansion along the crystallographic b-axis being substantially greater than along the other two axes.

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Temperature-induced polymorphism in methyl
stearate†
Cite this: DOI: 10.1039/c8ce01055b
a
c
*
X. Liu,
A. S. Gibbs,
G. S. Nichol, a C. C. Tang,b K. S. Knight,c
d
d
a
*
P. J. Dowding, I. More and C. R. Pulham
The crystallisation of methyl stearate under a range of crystallisation conditions has been studied and three
new polymorphs have been identified and structurally characterised. Form III (monoclinic, space group Cc,
Z = 8) was obtained at room temperature by slow evaporation of a saturated solution in CS2. Form IV
(monoclinic, space group C2/c, Z = 4) was obtained by slow cooling of the melt. Both structures were
characterised by single crystal X-ray diffraction. Form V (monoclinic, space group Cc, Z = 4) was obtained
from the melt by rapid cooling. X-ray and neutron powder diffraction methods were employed in the de-
termination of this structure. Form V shows highly anisotropic thermal expansion, with expansion along the
crystallographic b-axis being substantially greater than along the other two axes.
Received 27th June 2018,
Accepted 1st August 2018
DOI: 10.1039/c8ce01055b
rsc.li/crystengcomm
tallise. If the fuel remains cold for long periods of time, these
crystals can grow large enough in size to block engine filters
1. Introduction
Combustion of fossil fuels accounts for 98% of global carbon
dioxide emissions1 and so there is an urgent requirement to
reduce CO2 emissions by reducing consumption of these
fuels. Hence there is growing interest in the use of biofuels,
such as biodiesel, that are obtained from sustainable,
biomass-based sources. In 2003, the EU set a target for the
use of biodiesel of 5.75% of total fuel consumption by 2010,
whilst the current EU target for 2020 is 10%.2
Biodiesel mainly consists of a mixture of fatty acid methyl
esters (FAMEs) that are derived from vegetable oils or animal
fats (feedstocks) by transesterification reactions.3 Whilst bio-
diesel has some advantages as a fuel, it is well known that it
shows poor performance at low temperature.4 One disadvan-
tage is its poor cold-flow engine performance. For example, in
field studies, FAMEs derived from soybean oil began to solidify
when the environmental temperatures approached 0 °C.5 This
critical temperature is substantially higher than that of
petroleum-based diesels. When the environmental temperature
reaches the crystallisation temperature of diesel or biodiesel,
high-molecular weight components begin to nucleate and crys-
and injectors, causing very serious start-up and operational
problems for vehicles. Mitigation strategies have been demon-
strated through modification of the composition of biodiesel
by reducing the ratio of saturated/unsaturated FAMEs6,7 in or-
der to enhance the cold-flow performance. However, unsatu-
rated FAMEs are susceptible to oxidation even under ambient
conditions and indeed it has been shown that polyunsaturated
fatty acids are very prone to autoxidation.8–11 The degradation
of biodiesel not only significantly decreases the chain length of
the acid groups, leading to lower cetane number values,12,13
but can also produce organic acids and polymeric materials
that can potentially cause damage to engines. Given the grow-
ing importance of biodiesel and its associated problems at low
temperatures, it is therefore crucial to understand its
crystallisation behaviour in order to design efficient additives
that will improve its cold-flow performance. However, a major
challenge of such studies is presented by the nature of biodie-
sel – it is a complex mixture of multiple components with vari-
able compositions.13,14
A
better understanding of the
crystallisation behaviour of single components of biodiesel is
needed, hence the focus of this paper: the low-temperature
crystallisation behaviour of one of the main components of bio-
diesel, namely methyl stearate (C19H38O2).
Methyl stearate is a fully saturated methyl ester with a 17-
carbon linear chain (Fig. 1) and a melting point of 311 K.
a EaStCHEM School of Chemistry, University of Edinburgh, Edinburgh, EH9 3FJ,
UK. E-mail: Xiaojiao.Liu@ed.ac.uk
b Diamond Light Source Ltd, Harwell Science & Innovation Campus, Didcot,
Oxfordshire OX11 0DE, UK
c HRPD, ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot,
Oxfordshire OX11 0LA, UK
d Infineum UK Ltd, Milton Hill Business and Technology Centre, Abingdon, OX13
6BB, UK
† Electronic supplementary information (ESI) available. CCDC 1589573,
1811171–1811173. For ESI and crystallographic data in CIF or other electronic
format see DOI: 10.1039/c8ce01055b
Fig. 1 Molecular structure of methyl stearate.
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The crystal structure of methyl stearate has intrigued crys-
conducted without further purification of the sample. Initial
attempts focussed on repeating the experimental methods
described in ref. 16 and 17. Although it proved possible to
grow very thin crystals of methyl stearate in CS2 at low tem-
peratures, it proved impossible to manipulate and transfer
the crystals to the diffractometer without melting or dissolu-
tion. Instead, experiments were subsequently conducted that
involved (i) crystallisation from solution at ambient tempera-
ture, and (ii) crystallisation from the melt under both slow
and rapid cooling conditions. Neutron powder diffraction
studies were also conducted on the fully deuterated iso-
topomer of methyl stearate in order to corroborate the struc-
ture of the polymorph characterised by powder X-ray diffrac-
tion and to locate hydrogen positions.
tallographers for decades on account of the problems in
growing suitable quality single crystals for X-ray diffraction.
These difficulties arise from the nature of materials with long
hydro-carbon chains and reflect the tendency to form thin,
plate-shaped crystals with thicknesses of only
a few
microns.15 The first crystal structure of methyl stearate was
published in 1960, and was solved in the monoclinic crystal
system (A2/a) with unit cell parameters a = 5.61 Å, b = 7.33 Å,
c = 106.6 Å, β = 116.47° (form I).16 The paper reported that
single crystals were grown from CS2 solution at −15 °C to −12
°C, and X-ray diffraction data were collected at room temper-
ature. In 1970, MacGillavry grew single crystals and recorded
X-ray diffraction data under the same crystallisation and data
collection conditions, and reported a new orthorhombic
(Pnab) structure with unit cell parameters a = 5.613(5) Å, b =
7.354(5) Å, c = 95.417(4) Å (form II).17 Recently, a group from
the University of Leeds studied the morphology and growth
of methyl stearate as a function of crystallisation conditions
and rationalised the observed morphology on the basis of a
monoclinic form (space group C2) with unit cell parameters
a = 5.60 Å, b = 7.39 Å, c = 47.96 Å, β = 91.15°. However, no fur-
ther structural details were reported.18
2.1. Form III and form IV
Form III crystallised as colourless, thin, plate-like crystals
from a saturated solution of CS2 (Sigma Aldrich) at room
temperature by slow evaporation. A suitable specimen was se-
lected and mounted on a Rigaku Oxford Diffraction Super-
Nova diffractometer (Cu-Kα radiation, λ = 1.5418 Å). The crys-
tal was protected from melting during transfer to the
diffractometer by cooling in dry ice and it was subsequently
maintained at 120 K during data collection using an Oxford
Cryostream Plus.
Form IV was obtained from a finely ground, polycrystalline
sample of methyl stearate loaded into a borosilicate glass capil-
lary of 0.5 mm diameter. This was attached to a goniometer
head and mounted on a Rigaku Oxford Diffraction SuperNova
diffractometer (Mo-Kα radiation, λ = 0.7107 Å). The sample was
melted by warming to 323 K and the temperature was held for
10 min. It was then cooled at a rate of 5 K h−1 to 283 K to in-
duce nucleation and crystallisation of a single crystal, followed
by cooling to 120 K at a cooling rate of 360 K h−1. Single crystal
diffraction data were recorded at 120 K.
Form II contains one molecule in the asymmetric unit.
There are four molecular layers in the unit cell, packed in a
tilted manner and forming roof-like “ripples” along the c-axis
(Fig. 2a). The folding angle between the least squares planes
though the methyl stearate molecules is approximately 150°.
The ester groups (head) of the methyl stearate in one layer are
close to the ester groups of methyl stearate molecules in the
neighbouring layer, thereby packing in “head-to-head” bilayers.
In the crystallographic bc plane (Fig. 2b), the chain direction is
perpendicular to the lamella layers, and parallel with the c-axis.
Inter-chain interactions dominate packing behaviour.
Given the uncertainties in the literature about these poly-
morphs and the crystallisation conditions under which they
are formed, our aim was to explore the crystallisation of
methyl stearate under a wide range of conditions.
Unit cell parameters of form III and form IV (Table 1) were
obtained using the CrysAlisPro program.19 Olex2 software20
was employed for structure determination. Structures were
solved with the ShelXT21 program using Intrinsic Phasing
methods. Refinements were performed by ShelXL22 program
using least squares minimisation.
2. Experimental
High-purity methyl stearate (>99%) was obtained from Tokyo
Chemical Industry. The following experiments were
2.2. Form V
2.2.1. Synchrotron XRPD. High-resolution synchrotron
XRPD data were collected on beamline I11,23,24 at the Dia-
mond Light Source, UK, using an incident beam of wave-
length = 0.825795IJ7) Å. A polycrystalline sample of form V
was prepared by first quench-cooling the melt with liquid ni-
trogen, followed by gentle grinding at low temperature (Fig.
S1†). It was packed into a 0.5 mm borosilicate glass capillary
mounted on the spinner at the centre of the diffractometer.
The sample was cooled in situ on the diffractometer to 193 K
at a cooling rate of 360 K h−1 using an Oxford Cryostream
Plus. During cooling, rapid data collections (1 second per pat-
tern) were performed at intervals of 1 K using the position
Fig. 2 Packing plot of form II of methyl stearate. (a) View parallel to
the crystallographic b-axis; (b) view parallel to the crystallographic
c-axis.
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Table 1 Crystal data and refinement details of different forms of methyl stearate
Form I16
Form II17
Form III
Form IV
Form V
Space group
Monoclinic
A2/a
Orthorhombic
Pnab
Monoclinic
Cc
Monoclinic
C2/c
Monoclinic
Cc
a (Å)
b (Å)
c (Å)
β (°)
V (Å3)
Z
5.610
7.330
106.600
116.78
3913.37
8
5.613(6)
7.354(5)
95.147(4)
90
3927.48(3)
8
95.583(8)
7.291(8)
5.586(4)
92.57(1)
3889.6(5)
4
47.795(13)
7.113(4)
5.532(4)
90.48(3)
1880.49(5)
8
49.013(1)
7.213(1)
5.556(1)
77.536(2)
1917.78(7)
4
Z′
1
1
2
0.5
1
R
R1 = 0.1543
wR2 = 0.4416
120
R1 = 0.1160
wR2 = 0.3129
120
Rwp = 0.11076
Rexp = 0.0240
193
Collection temperature (K)
∼293
∼293
sensitive detector (PSD). Once the sample temperature had
stabilised at 193 K, 30 min data collections were performed
using the 45 multi-analysing crystal (MAC) detectors to ob-
tain high resolution data (small angular step of 0.001° high
signal-to-noise ratio) for structure solution.
and used without further purification. All reactions were
performed in oven-dried glassware.
Preparation of the NaHSO4·SiO2 catalyst26. 10 g of SiO2
(column chromatographic grade, 60 Å, 200–400 mesh) was
added to a solution of 4.14 g (0.03 mole) of NaHSO4 in
20 mL of water. After stirring for 15 min at room
temperature, the mixture was gently heated on a hot plate
(50 °C) with stirring, until a free-flowing white solid was
obtained. The solid was then dried in an oven at 120 °C
for 48 h prior to use.
A 2θ range from 1–29° was used for indexing diffraction
patterns (Table 1) using Topas 4.1.25 The space group was de-
termined as Cc. The following unit cell parameters were
obtained at 193 K: a = 49.012(8) Å, b = 7.212(2) Å, c =
5.555(10) Å, β = 77.527IJ6)°; good values of Rwp = 9.324%, Rexp
= 2.262% and GoF = 4.121 were obtained. Initially, the struc-
ture solution indicated that the 17-carbon chain in methyl
stearate was partly disordered and so in order to obtain reli-
able structural coordinates from the XRPD pattern, distance-
and angle-restrained refinements with non-hydrogen atoms
were performed simultaneously using Rietveld refinement.
All hydrogen atoms were added in calculated positions. The
final fit of the Rietveld refinements is shown in Fig. 3: the
difference plot, combined with the figures of merit (Table 1),
confirm the excellent fit obtained.
Preparation of perdeuterated methyl stearate. Deuterated
stearic acid was kindly provided by the ISIS Deuteration
Facility. 5 g of deuterated stearic acid was added to 300 mL
methanol-d4 (≥99.8 atom %D) in a 500 mL round-bottomed
flask with 5.5 g of NaHSO4·SiO2 prepared as described above.
The flask was sealed with Parafilm M and the contents
stirred at 45 °C. This was based on a procedure described in
ref. 27, but conducted at the higher temperature of 45 °C in
order to increase the reaction rate. The reaction (Scheme 1)
was monitored by 13C NMR (recorded in CHCl3) until the
peak of the acid group of deuterated stearic acid (δ = 182
ppm) was no longer visible. The mixture was cooled and fil-
tered under vacuum, and the recovered catalyst was washed
with deuterated methanol (10 mL). The combined solution
was concentrated in vacuo to obtain the required product as
a white solid.
2.2.2. Neutron powder diffraction
2.2.2.1. General sample preparation. Unless otherwise
indicated, all reagents were purchased from Sigma Aldrich
2.2.2.2. Data collection and analysis. High-resolution
neutron powder diffraction data of perdeuterated methyl
stearate were collected on the high resolution powder
diffractometer (HRPD), at the ISIS Neutron Facility, STFC-
Rutherford Appleton Laboratory, UK. A polycrystalline sam-
ple was prepared following the preparation method of the
sample used for synchrotron XRPD studies as described
above. 2 g of the sample was gently packed into a vanadium
slab can before being cooled to 4.2 K in situ on the diffrac-
tometer. Data were collected simultaneously using the back-
scattering detector banks, the 90° banks, and the low-angle
banks (2θ = 30°) over the time-of-flight range 30–130 ms.
Fig. 3 Rietveld refinement of synchrotron XRPD data of form V of
methyl stearate collected at 193 K on beamline I11. The experimental
(black), calculated profile (red) and difference (blue). Vertical tick marks
(pink) show calculated peak positions. The arbitrary unit of (a) is 24
times of the unit of (b).
Scheme 1 Synthesis of perdeuterated methyl stearate.
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Data were then collected upon warming the sample from 4.2
K to 300 K and then cooling to 10 K for 20 min intervals,
holding the sample at each required temperature for 10 min
in order to allow thermal equilibration before data collec-
tion. Long data collections (8 h) were conducted at 4.2 K,
193 K, and 300 K. On account of the large crystallographic
unit cell of methyl stearate, only the diffraction patterns
recorded by the backscattering detector (centred around
168°) and the complementary detector at 90° were employed
in the structural analysis.
Rietveld refinement of the crystal structure was conducted
using the GSAS program27 and used as its starting point the
structure of form V of methyl stearate solved from XRPD
data. Bond length and bond angle restraints were imposed
on the ester group of methyl stearate. The final profile fits of
calculated patterns compared to recorded diffraction patterns
are shown in Fig. 4. The crystallographic data and details of
the Rietveld refinement are given in Table 1.
3. Results and discussion
3.1. Form III
The crystal structure of form III of methyl stearate contains
two independent molecules (A and B) in the asymmetric unit
(Fig. 5). The two molecules differ essentially in the conforma-
tion of the ester groups. The CI–O1–C2–O2 torsion angle is
−5.8° in the molecule A, while the CIA–O1A–C2A–O2A torsion
angle is 3.3° in the molecule B. The bond angle O2–C2–O1 in
Fig. 4 Rietveld refinement plot of neutron powder data of form IV of
methyl stearate collected at 193 K on the HRPD instrument. The
experimental (black), calculated profile (red) and difference (blue).
Vertical tick marks (pink) show calculated peak positions. (a) A plot of
pattern recorded by the backscattering detector (bank 1); (b) a plot of
pattern recorded by the complementary detector at 90° (bank 2).
molecule
hybridised carbon atom. However, the corresponding bond
angle in molecule (O2A–C2A–O1A refines as 112.3°,
A
is 120.9°, as expected for the central sp2
B
)
suggesting some degree of packing disorder.
There are four molecular layers showing tilted packing in
the unit cell (Fig. 6a). Unlike in form II, the “head-to-head”
bilayers in form III that arise from the two independent
asymmetric methyl stearate molecules form oblique layers
with the same tilt angles with the crystallographic bc plane (1
0 0). The repeat bilayer thickness (C19A–C19 distance) is 44.93
Å. The thicknesses of the single layer A (C1–C19 distance) and
B (C1A–C19A distance) are 21.23 Å and 21.26 Å, respectively.
The gap between layer A and layer B is 2.44 Å (C1–C1A dis-
tance), while the distance between two bilayers is 2.81 Å. The
tilt angle of the least squares line through molecule A with
respect to the bilayer normal (where the bilayer plane is de-
fined by the least squares plane of C19 atoms) is 55.6°,
whereas the corresponding angle for molecule B is 56.2°. In
the crystallographic ab plane (Fig. 6b), the chain direction is
perpendicular to the lamella layers, parallel with the a-axis.
The packing behaviour is also dominated by inter-chain
interactions.
consists of half a molecule of methyl stearate with disorder
of the ester head group caused by inversion symmetry.
Chains of molecules of methyl stearate pack in homolo-
gous, oblique layers, parallel to the crystallographic bc plane.
(Fig. 7a) The least-squares line through the molecule forms a
42° tilt angle with the crystallographic ab plane. In the ab
plane (Fig. 7b), the chain direction is perpendicular to the la-
mella layers, parallel with the a-axis. The packing behaviour
is also dominated by inter-chain interactions.
3.2. Form IV
The crystal structure was refined in space group C2/c with a
crystallographically-imposed inversion centre located at the
centre point of the C10–C10 bond. The asymmetric unit thus
Fig. 5 The two independent molecules in the asymmetric unit of the
crystal structure of form III (view along the b-axis).
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Table 2 Details of the Rietveld refinements for the synchrotron XRPD
and NPD data of form V of methyl stearate (X-ray – non-deuterated; neu-
tron – fully deuterated)
Parameters
X-ray (synchrotron)
Neutron
a (Å)
b (Å)
c (Å)
49.013(1)
7.213(1)
5.556(1)
77.536(2)
1917.78(7)
Cc
48.947(2)
7.198(1)
5.547(1)
77.453(1)
1907.60(3)
Cc
β (°)
V (Å3)
Space group
Fig. 6 Packing plot of form III of methyl stearate. (a) View along the
b-axis, shown without hydrogen atoms (distances between each plane
are labelled, the planes of the boundaries of bilayers are shown in pink
while those of single layers are shown in blue); (b) view along the
c-axis, hydrogen atoms are shown in calculated positions.
Z
R
4
4
Rwp = 0.11076
Rexp = 0.0240
193
Rwp = 0.0169
Rp = 0.0179
193
T (K)
3.3. Form V
13.98° tilt angle with crystallographic ab plane. A change of
packing behaviour of methyl stearate has been clearly ob-
served. Unlike the “head to head” bilayer packing in form II
and III, a “head to tail” monolayer structure was observed in
form V of methyl stearate. In the crystallographic bc plane,
(Fig. 8b) the chain direction is perpendicular to the lamella
layers, parallel with the c-axis. The packing behaviour is also
dominated by inter-chain interactions.
3.3.1. Crystal structure. Whilst the proposed structure of
form V obtained from the XRPD studies is plausible, on ac-
count of the complex structure and the relative insensitivity
of X-rays to scattering from hydrogen atoms there initially
remained some doubt about whether this structure was in
fact correct. It was for this reason that complementary neu-
tron powder diffraction studies were performed.
3.3.2. Thermal expansion behaviour. Having determined
the crystal structure of form V of methyl stearate at 193 K,
high-resolution XRPD and neutron powder diffraction studies
were extended to investigate the thermal expansion behaviour
of form V of methyl stearate and explore whether any new
forms could be identified at different temperatures.
These show excellent agreement with the XRPD studies
(Table 2) thereby confirming that this is indeed the correct
structure. The small differences in unit-cell volumes between
perdeuterated and hydrogenous samples reflect the well-
known geometric isotope effect (GIE)28–30 in which E–D bond
lengths are slightly shorter that E–H bonds. This geometrical
H/D isotope effect is also particularly striking for materials
that are dominated by hydrogen-bonding interactions that
stabilise crystallographic packing.31 Although clearly in the
case of methyl stearate there is no hydrogen bonding, and
hence the origin of the smaller unit-cell volume for the
perdeuterated compound is simply the shorter C–D bond
length compared to the C–H bond length.
The crystal structure of form V of methyl stearate has one
molecule in the asymmetric unit. The packing behaviour is
similar to that of form III. However, there are two molecular
layers in the unit cell. Molecules of methyl stearate pack in
oblique chain layers, parallel to the crystallographic bc plane.
(Fig. 8a) The least squares line though the molecule forms a
Unit cell parameters over a range of temperatures of hy-
drogenous and deuterated samples of form V of methyl stea-
rate are tabulated in the ESI† (Tables S1 and S2). The relative
thermal expansions of the unit cell parameters are shown in
Fig. 9a (deuterated) and Fig. 9b (hydrogenous), and highlight
the highly anisotropic thermal expansion of methyl stearate.
For the monoclinic crystal system, one of the principal axes
of the thermal expansion coincides with the crystallographic
b-axis.32 The other two principal axes are in the (0 1 0) plane.
Fig. 9 shows clearly that the unit cell b-axis of form V in-
creases significantly more with temperature than do the
c-axis and the β angle. The crystallographic a-axis remains al-
most constant over the entire temperature range. A likely ex-
planation for this is that the molecules of methyl stearate lie
along the a-axis, and so the length of the a-axis is dominated
Fig. 7 Packing plot of methyl stearate form IV. (a) View along the
b-axis, shown without hydrogen atoms, torsion angles and distances
between least-square planes are labelled; (b) view along the c-axis,
shown with partially disordered hydrogen atoms.
Fig. 8 Packing plot for form V of methyl stearate. (a) View parallel to
the b-axis, shown without hydrogen atoms; (b) view parallel to the
c-axis, shown with deuterium positions.
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The fit (shown in Fig. 10) resulted in the values θD = 189 14
K, θE = 1287 186 K, V0 = 1842.4 0.4 Å3, A1 = 4.17 0.03 × 104 J
cm−3, A2 = 1.78 1.04 × 103 J cm−3. The Debye temperature
obtained (≈189 K) is consistent with those of other low-
dimensional organic compounds.34,35 The relatively large errors
in the fitted parameters for the Einstein component of the
model can largely be accounted for by the restricted experimen-
tal temperature range in relation to the Einstein temperature.
No anomalies in the thermal expansion behaviour were detected
within the temperature resolution of these experiments.
It was possible to compare the different thermal expan-
sion coefficients of the lattice parameters induced by deutera-
tion over the temperature range 193–280 K. The thermal ex-
1 L
L0 T


pansion coefficients of both axial
and
L 






1
V
T



p
volumetric
are calculated and tabulated in






V

V
0 


Table 3. This shows that the thermal expansion behaviour of
hydrogenous and deuterated methyl stearate is very similar
over this temperature range. It is interesting to note that
thermal expansion coefficients of all the unit cell parameters
of the deuterated methyl stearate are slightly higher than
those for the hydrogenous sample. This suggests that the
intermolecular interactions in deuterated methyl stearate are
slightly weaker than those of the hydrogenous sample.
3.3.3. Identification of a further phase. It is interesting to
note that when the temperature was increased to 300 K, there
was some evidence of changes shown in the neutron powder
patterns of at 300 K (see Fig. S4a and S5A in ESI†), which sug-
gest that deuterated methyl stearate underwent a phase tran-
sition over the temperature range 280–300 K from form V to
an unknown polymorph denoted as form VI. Visual inspec-
tion of the patterns collected during temperature decrease
suggests that form VI persisted when the temperature was de-
creased (see Fig. S4b and S5B in ESI†).
Fig. 9 Multiplots of the relative unit cell expansion of form V of
methyl stearate. (a) Deuterated methyl stearate over the temperature
range of 4.2 K to 280 K (neutron data); (b) hydrogenous methyl
stearate over the temperature range of 193 K to 298 K (synchrotron
X-ray data).
by C–C covalent bonds within the hydrocarbon chains. These
are relatively rigid and so would not be expected to be
strongly affected by temperature changes. In contrast, along
the b-axis there are only very weak intermolecular interac-
tions between chains of molecules and so thermal expansion
is substantially greater along this direction.
The temperature dependence of the unit cell volume of deu-
terated methyl stearate in the temperature range of 4.2 K to
280 K was fitted to a Debye–Einstein model33 (eqn (1) and (2))
It was possible to perform Rietveld refinements for form
VI based on the high quality NPD data. The structure of form
UD
T
UE
T
 
 
V T V 
 

(1)
0
A
A2
1



3

D
T
0
T
x3
ex 1
3NkBE
V T V  9Nk T
 
dx A 
A2
(2)
0
B
1
E
D

e T 1
where kB is Boltzmann's constant, θD is the characteristic De-
bye temperature and θE is the characteristic Einstein temper-
ature. x = ħω/kBT, N is the number of atoms in the unit cell,
A1 and A2 = KT/γ (KT is the isothermal bulk modulus, γ is the
Grüneisen ratio).
Fig. 10 Volume thermal expansion coefficient of form V of deuterated
methyl stearate fitted to a Debye–Einstein model.
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Table 3 Comparison of the thermal expansion coefficients of unit cell parameters of form V of hydrogenous (193 K to 298 K) and deuterated methyl
stearate (193 K to 280 K)
Sample type
αa (× 10−6 K−1
)
αb (× 10−4 K−1
)
αc (× 10−5 K−1
)
αβ (× 10−5 K−1
)
αV (× 10−4 K−1
)
Hydrogenous
Deuterated
2.91(4)
4.29(1)
2.28(1)
2.50(1)
7.02(3)
7.39(1)
4.54(4)
4.90(6)
3.16(4)
3.40(7)
V of deuterated methyl stearate at 193 K, solved from neutron
powder diffraction, was employed as a model. Comparison of
Rietveld refinements performed on the data collected at 280
K and 300 K (Fig. 11) highlights the phase change. In particu-
lar, it is notable that a number of reflections (such as Bragg
peaks at d-spacings of 1.27 Å, 2.22 Å, and 2.39 Å) shown in
the patterns collected at 300 K, could not be fitted by the
model structure of form V, or indeed any of the known
forms. Unfortunately, on account of the large unit cell vol-
umes of the polymorphs of methyl stearate, combining with
the limited d-spacing range of the data recorded from HRPD
instrument, it was not possible to determine the unit cell pa-
rameters of form VI. Moreover, this transition was not ob-
served in the PXRD pattern of the hydrogenous sample at the
maximum temperature of 298 K. This strongly suggests that
there may be an effect of deuteration, either on the formation
of form VI or on the transition temperature. An alternative ex-
planation is that this phase transition is associated with a
rearrangement of some of the hydrogen (deuterium) atoms.
This would appear clearly in the neutron experiment, which
is very sensitive to scattering from deuterium atoms, but
might not appear in the X-ray experiment on account of the
only weak contribution to the scattering from hydrogen
atoms.
gle between molecules inside the bilayer. In form II, which
crystallised under low temperature, methyl stearate mole-
cules stack in roof-like “waves” with an approximately open
3.3.4. Wider context. Von Sydow has previously noted that,
in general, methyl esters of odd-numbered acids have two
crystalline forms.36 One is a dimeric form with a tilt angle of
67.5° between the hydrocarbon chain and the basal plane,
which contains the end groups of the molecule. The other
form is monomeric, with a tilt angle of 75.0°. Methyl esters
of even-numbered fatty acids only have one dimeric form
with a tilt angle of 63.0°,36 except methyl stearate and methyl
palmitate which have two crystalline forms with different
melting points with only a few degree apart. The formation
of two different forms depends on the rate of the
crystallisation.37 Clearly, based on the results of the current
study, the crystallisation of methyl stearate is substantially
more complex and is significantly temperature-dependent.
Differences in the structures of the polymorphs described in
the current work are reflected in the packing of the terminal
methyl group (“tail”) of methyl stearate. The end-group pack-
ing behaviour has a significant effect on the overall crystal
structures.
Fig. 11 Rietveld refinements of the neutron powder patterns collected
at 280 K and 300 K, using form V of deuterated methyl stearate as
model structure, show mismatched peaks induced by the phase
transition. In both cases the experimental profile (black), calculated
profile (red) and difference (blue). Vertical tick marks (pink) show
calculated peak positions. Blue arrows indicate mismatching
Forms II and III were both obtained from a CS2 solution
and show some degree of similarity in molecular packing.
Methyl stearate molecules in these two forms all pack in
“head to head” (and “tail to tail”) oblique bilayers, with four
molecular layers in the unit cell. The most significant differ-
ence between the structures of form II and III is the tilt an-
reflections. (a)
a plot of pattern recorded by the backscattering
detector (bank 1); (b) a plot of pattern recorded by the complementary
detector at 90° (bank 2).
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120° angle between the least squares line though the methyl 4. Conclusions
stearate moieties. By contrast, in form III, which was
This research has shown that the crystallisation behaviour of
methyl stearate is strongly affected by temperature. A new
polymorph, form III, was successfully obtained by growing a
single crystal from a saturated CS2 solution at room tempera-
ture and data collection was conducted at 120 K. Form IV
was obtained by crystallisation from the melt followed by
slow cooling. Structural characterisation using single crystal
X-ray diffraction showed disordered packing of the molecules
in this form. The crystal structure of form V, obtained by
quench cooling from the melt, was solved and refined using
a combination of synchrotron XRPD and high-resolution neu-
tron powder diffraction. The thermal expansion behaviour of
this form was also investigated. Form V of methyl stearate
shows highly anisotropic thermal expansion, with signifi-
cantly greater expansion along the crystallographic b-axis
compared to the a- and c-axes. The deuterated sample
showed a higher volume thermal expansivity. The crystal
structure of form III shows “head to head (ester group)” bi-
layer packing behaviour with similar unit cell parameters as
published for form II. Differences are shown in packing an-
gles of molecules between layers. Forms IV and V show simi-
lar monolayer packing behaviours with similar unit cell pa-
rameters but unlike form III, form V are shown “head to tail
(end of chain group)” packing, while the length of crystallo-
graphic axis of form V along hydrocarbon chain accommoda-
tion only shows half of those of form III. In contrast to form
V, form IV structure has a crystallographic inversion centre
located in the centre of the molecule and the whole structure
exhibits whole molecule disorder. Furthermore, a phase tran-
sition from form V to form VI (280–300 K) was observed in
the neutron diffraction experiments for a fully deuterated
sample, but no evidence for this transition was observed
from a hydrogenous sample in a corresponding synchrotron
XRPD study.
crystallised at room temperature, the open angle between
the methyl groups of adjacent layers is 180°. Both form IV
and V were crystallised from the melt, but using different
cooling rates. They both exhibit tilted monolayers, with two
molecular layers in the unit cell, while as forms II and III,
show bilayer packing behaviour leading to a doubled crystal-
lographic axis along with direction of the hydrocarbon
chain.
A similar difference in packing has also been
reported for long-chain alkanes;15,38 it was suggested that
this difference could be induced by the presence of impuri-
ties at a level of 2% being required for the formation of bi-
layers. In this case, the solvent could possibly act as an im-
purity inducing the layer doubling, although we saw no
evidence of incorporation of CS2 in these studies. Another
possibility of the difference of the packing behaviour may
be induced by the conformation of the material its polarity.
Methyl stearate contains hydrophobic hydrocarbon chain
and a more hydrophilic ester group. It is therefore more
likely to form lipid bilayers in solution due to the hydropho-
bic interactions. The structure obtained from CS2 solution
therefore shows “head to head” packing. In contrast, this
cannot happen on crystallisation from the melt. This type
of “head to head” packing of methyl stearate could give
some into the design of additives for biodiesel. Given that
biodiesel contains FAME compounds dissolved in hydrocar-
bons, it is therefore likely that crystallites formed under
low-temperature conditions will feature packing that in-
volves the formation of “head-to-head” bilayers.
Different cooling rates of the melt clearly influence the
outcome of crystallisation. Form IV, which was crystallised
by slow cooling, shows a highly disordered structure, in
contrast to form
V which was crystallised by rapid
cooling. This is perhaps a somewhat surprising result as
one would normally expect rapid quenching of a melt to
result in structures that are more disordered. The disor-
dered packing behaviour of form IV suggests that it is
less stable than form V.
Conflicts of interest
The packing behaviour in all of the polymorphs is domi-
nated by inter-chain interactions, which appear to be weaker
for deuterated methyl stearate compared to the hydrogenous
sample.39 This is clearly shown in the significant difference
in thermal expansion coefficients of the two isotopomers over
a similar temperature range and is perhaps a possible expla-
nation as to why the phase transition observed in the deuter-
ated sample from form V to VI was not observed in the hy-
drogenous sample over the same temperature range. Finally,
we should comment on the almost identical lattice parame-
ters of form IV identified in this study and the monoclinic
form reported in ref. 18. The only difference is in the assign-
ment of space group (C2/c for form IV compared with C2 in
the previous report). Given the consistency between the struc-
tures of form IV determined by both X-ray and neutron tech-
niques, there is a high degree of confidence that the space
group is indeed C2/c rather than C2.
There are no conflicts to declare.
Acknowledgements
The authors grateful acknowledge Infineum Ltd. for
funding this research. We thank Diamond Light Source for
access to beamline I11 (NT12259-1) that contributed to the
results presented here. We gratefully acknowledge the Sci-
ence and Technology Facilities Council (STFC) for access
to neutron beamtime at ISIS, and also for the provision of
sample preparation, HRPD facilities. Many thanks to Prof
Ken Lewtas, Dr Sumit Konar, Dr Adam Michalchuk, Dr
Katrina Warrack, Dr Boris Zakharov, and Dr Peter Hutch-
ins for helpful discussions. X. Liu is grateful for an Edin-
burgh Global Research Scholarship and PhD studentship
funding from Infineum Ltd.
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